Do they really matter that much? I'm just using skate shoes for squating because I remember reading somewhere that the flat soles would be the best. I switched from running shoes because I didn't find them comfortable.
i say that because if they're stable, the worst that will happen is they'll absorb some of the force you exert by compressing. chucks and oly shoes aren't too cushiony, that's part of why they work well for squatting.